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Compilers have focused on the exploitation of one of functional or data parallelism in the past. The PARADIGM compiler project at the University of Illinois is among the first to incorporate techniques for simultaneous exploitation of both. The work in this paper describes the techniques used in the PARADIGM compiler and analyzes the optimality of these techniques. It is the first of its kind to use realistic cost models and includes data transfer costs which all previous researchers have neglected. Preliminary results on the CM-5 show the efficacy of our methods and the significant advantages of using functional and data parallelism together for execution of real applications.